The G-differentiability and geometric properties of the Zadeh extensions of functions

In this paper, the concepts of right G-derivative, left G-derivative and G-derivative (with respect to a direction) of fuzzy number mappings are introduced, and some properties of continuity, monotonicity, convexity (or concavity) and G-differentiability of fuzzy number mappings are given. After that, the continuity, monotonicity and convexity (or concavity) of the Zadeh extensions F (is restricted to fuzzy number space E) of a function f are characterized by the continuity, monotonicity and convexity (or concavity) of f, respectively.